Question

how many triangles do you see in figure.

Answer 1

overlapping or no?

Answer 2

overlapping

Answer 3

39?

Answer 4

43 or 45

Answer 5

43-45

Answer 6

44 i think

Answer 7

let's see,
we have 1 huge triangle

Answer 8

the no of smallest triangle is 9+7+5+3+1 = 26

Answer 9

a little bigger triangle .. we have 13, so total is 40 until now

Answer 10

45 is the answer

Answer 11

no .. but quite close

Answer 12

i think 46

Answer 13

Oo... sorry @King 's right i made mistake in above summation

Answer 14

can you explain your approach?

Answer 15

so 45 is rite?

Answer 16

9+7+5+3+1 = 26 .. from this i was able to deduce 46

Answer 17

nos.of small triangles=25 not 26!!@experimentX

Answer 18

9+7=16
5+3+1=9
16+9=25!!

Answer 19

still i cannot come up with general formula ...!

Answer 20

I got 46

Answer 21

no.of triangles=level of @experimentX

Answer 22

hw diya?

Answer 23

Wait letme count again

Answer 24

lol ... quite a matching no.

Answer 25

no.of small triangles=25
no.of triangles with 2 rows of small triangles=10
no.of triangles with 3 rows of small triangles=6
no.of triangles with 4 rows of small triangles=3
1 big full triangle
so,
25+10+6+3+1
=45!!

Answer 26

no.of triangles with 2 rows of small triangles=10 ...it think this should be 13, aren't we missing inverted triangles?

Answer 27

If overlapping I found 45

Answer 28

yeah!!sry so its 48

Answer 29

not include the inverted ones :(

Answer 30

there are no inverted ones wid 3 or 4 rows so it has to be 48...i think

Answer 31

so answer is 48!!

Answer 32

@experimentX u der?if u are happy and satisfied wid answer close the question....

Answer 33

i guess 48 is the right answer ...

Answer 34

still i was looking some sorts of permutations and combinations to this get this answer ... anyway thanks to all who tried.

Answer 35

floor(n(n+2)(2n+1)/8)
where n is the number of triangles on a side
in your specific case, n=5

Answer 36

if this problem is only about the dark triangles it is kind of boring...
isn't it about using the inverted ones as well as callisto suggested?

Answer 37

actually, I'm seeing more problems with the solution here
isn't there much more going on that we are ignoring?

Answer 38

@philips13 Gave the right answer.

\[\huge \lfloor \normalsize \frac{ (n(n+2)(2n+1)}8 \huge \rfloor \]

Answer 39

Oh yeah?
Ok thanks, but now I wanna decipher it
you seem to be familiar with this theorem FFM :P

Answer 40

I am familiar with almost everything labelled interesting :P

http://www.mathematik.uni-bielefeld.de/~sillke/SEQUENCES/grid-triangles

Answer 41

You think we haven't noticed?
Where do you get this encyclopedic knowledge?!

Answer 42

Lol, I was kidding. I am just an ordinary guy with some practice :)

Answer 43

yeah, whatever... :P
I'm not sure I understand some of the notation on the link you gave me, but I'm sure I'll get it after hacking away at it for a while.
Thanks :D

Answer 44

:)

Answer 45

I was thinking why i couldn't get the answer 48 when i did the calculation. But then from the website, it says that
number of triangle
= n*(n+2)*(2n+1)/8 for n even
= (n*(n+2)*(2n+1) - 1)/8 for n odd
So, I got 48 finally...
BTW, it's experimentX who first suggested that we were missing the inverted triangles

Answer 46

thanks to all for reply!! and finally it's complete!

Answer 47

48 i guess